Flexural vibration piece and oscillator using the same

ABSTRACT

A flexural vibration piece includes: a flexural vibrator that has a first region on which a compressive stress or a tensile stress acts due to vibration and a second region having a relationship in which a tensile stress acts thereon when a compressive stress acts on the first region and a compressive stress acts thereon when a tensile stress acts on the first region, and performs flexural vibration in a first plane; and a heat conduction path, in the vicinity of the first region and the second region, that is formed of a material having a thermal conductivity higher than that of the flexural vibrator and thermally connects between the first region and the second region, wherein when m is the number of heat conduction paths, α th  is the thermal conductivity of the heat conduction path, α v  is the thermal conductivity of the flexural vibrator, t v  is the thickness of the flexural vibrator in a direction orthogonal to the first plane, and t th  is the thickness of the heat conduction path, a relationship of t th ≧(t v /m)×(α v /α th ) is satisfied.

BACKGROUND

1. Technical Field

The present invention relates to a flexural vibration piece thatvibrates in a flexural mode and an oscillator using the same.

2. Related Art

As a flexural vibration piece that vibrates in a flexural mode in therelated art, a tuning fork-type flexural vibration piece has been widelyused in which a pair of vibration arms are extended in parallel to eachother from a base formed of a base material such as a piezoelectricmaterial and are caused to horizontally vibrate toward each other andaway from each other. When the vibration arms of the tuning fork-typeflexural vibration piece are excited, the occurrence of the vibrationenergy loss causes a reduction in performance of the vibration piece,such as an increase in CI (Crystal Impedance) value or a reduction in Qvalue. For preventing or decreasing such a vibration energy loss,various measures have been taken in the related art.

For example, a tuning fork-type quartz vibration piece has been known inwhich a notch or a notch groove having a predetermined depth is formedon both side portions of a base from which vibration arms extend (forexample, refer to JP-A-2002-261575 and JP-A-2004-260718). In the tuningfork-type quartz vibration piece, when the vibration of the vibrationarms includes also a vertical component, the notch or the notch groovereduces the leakage of vibration from the base. Therefore, theconfinement effect of vibration energy is enhanced to control the CIvalue and prevent irregularities in CI values between vibration pieces.

In addition to the mechanical vibration energy loss, vibration energyloss is also caused by heat conduction due to the temperature differencecaused between a compression portion on which a compressive stress ofthe vibration arms that perform flexural vibration acts and an extensionportion on which a tensile stress acts. A reduction in Q value caused bythe heat conduction is called a thermoelastic loss effect.

For preventing or suppressing the reduction in Q value due to thethermoelastic loss effect, a tuning fork-type vibration piece in which agroove or a hole is formed on the center line of vibration arms(vibration beams) having a rectangular cross section is disclosed in,for example, JP-UM-A-2-32229.

JP-UM-A-2-32229 describes, based on a well-known relational formulabetween strain and stress in the case of internal friction in solidsgenerally caused by temperature difference, that in the thermoelasticloss in a vibration piece in a flexural vibration mode, the Q valuebecomes minimum in the case where the number of relaxation oscillationsfm=1/(2πτ) (where τ is a relaxation time) when the number of vibrationschanges. The relationship between the Q value and frequency generallyexpressed as the curve F in FIG. 11 (for example, refer to C. Zener andother two persons, “Internal Friction in Solids III. ExperimentalDemonstration of Thermoelastic Internal Friction”, PHYSICAL REVIEW, Jan.1, 1938, Volume 53, p. 100-101). In the drawing, the frequency at whichthe Q value takes a minimum value Q₀ is a thermal relaxation frequencyf₀ (=1/(2πτ)), that is, the thermal relaxation frequency f₀ is the sameas the number of relaxation oscillations fm.

Description will be made specifically with reference to the drawing. InFIG. 10, a tuning fork-type quartz vibration piece 1 of JP-UM-A-2-32229includes two vibration arms 3 and 4 extending from a base 2 in parallelto each other. The vibration arms 3 and 4 are provided with lineargrooves or holes 6 and 7 on the respective center lines. When apredetermined drive voltage is applied to a not-shown excitationelectrode of the tuning fork-type quartz vibration piece 1, thevibration arms 3 and 4 perform flexural vibration toward each other andaway from each other as indicated by imaginary lines (two-dot chainlines) and arrows in the drawing.

Due to the flexural vibration, a mechanical strain occurs in regions ofroot portions of the respective vibration arms 3 and 4 at the base 2.That is, in the root portion of the vibration arm 3 at the base 2, afirst region 10 on which a compressive stress or a tensile stress actsdue to the flexural vibration and a second region 11 having arelationship in which a tensile stress acts thereon when a compressivestress acts on the first region 10 and a compressive stress acts thereonwhen a tensile stress acts on the first region 10 are present. In thefirst region 10 and the second region 11, temperature increases when acompressive stress acts, while temperature decreases when a tensilestress acts.

Similarly, in the root portion of the vibration arm 4 at the base 2, afirst region 12 on which a compressive stress or a tensile stress actsdue to the flexural vibration and a second region 13 having arelationship in which a tensile stress acts thereon when a compressivestress acts on the first region 12 and a compressive stress acts thereonwhen a tensile stress acts on the first region 12 are present. In thefirst region 12 and the second region 13, temperature increases when acompressive stress acts, while temperature decreases when a tensilestress acts.

Due to the thus generated temperature gradient, inside the root portionsof the respective vibration arms 3 and 4 at the base 2, heat conductionoccurs between the first region 10 and the second region 11 and betweenthe first region 12 and the second region and 13. The temperaturegradient is generated in opposite directions corresponding to theflexural vibration of the vibration arms 3 and 4, and also the heatconduction changes in direction corresponding thereto. Due to the heatconduction, part of the vibration energy of the vibration arms 3 and 4is constantly lost during vibration as thermoelastic loss. As a result,the Q value of the tuning fork-type quartz vibration piece 1 decreases,which makes it difficult to realize a desired, high performance. In thetuning fork-type quartz vibration piece 1 disclosed in JP-UM-A-2-32229,heat transfer from a compression side to a tensile side is blocked bythe grooves or holes 6 and 7 disposed on the respective center lines ofthe vibration arms 3 and 4, so that the decrease in Q value due to thethermoelastic loss can be prevented or diminished.

However, in the tuning fork-type quartz vibration piece 1 disclosed inJP-UM-A-2-32229, it becomes difficult along with miniaturization to formthe grooves or holes having a shape by which a reduction in Q value dueto the thermoelastic loss can be prevented or reduced. In addition,there might be a problem that an effect of suppressing the reduction inQ value cannot be sufficiently provided.

SUMMARY

An advantage of some aspects of the invention is to solve at least apart of the problem and can be realized as the following aspects orapplications.

First Application

A first application of the invention is directed to a flexural vibrationpiece including: a flexural vibrator that has a first region on which acompressive stress or a tensile stress acts due to vibration and asecond region having a relationship in which a tensile stress actsthereon when a compressive stress acts on the first region and acompressive stress acts thereon when a tensile stress acts on the firstregion; and a heat conduction path, in the vicinity of the first regionand the second region, that is formed of a material having a thermalconductivity higher than that of the flexural vibrator and thermallyconnects between the first region and the second region, wherein when mis the number of heat conduction paths, α_(th) is the thermalconductivity of the heat conduction path, α_(v) is the thermalconductivity of the flexural vibrator, t_(v) is the thickness of theflexural vibrator in a direction orthogonal to a vibration direction ofthe flexural vibrator, and t_(th) is the thickness of the heatconduction path in the direction orthogonal to a vibration direction ofthe flexural vibrator, a relationship of t_(th)≧(t_(v)/m)×(α_(v)/α_(th))is satisfied.

The present inventor has found that according to the configuration, athermal relaxation time required for the temperature difference causedbetween the first region and the second region reaching a state ofequilibrium is shortened due to the heat conduction path having athermal conductivity higher than that of the flexural vibrator, andtherefore a reduction in Q value is suppressed.

Since the heat conduction path can be disposed without forming the holeor groove in the flexural vibrator unlike the related-art measuresdescribed above, the configuration is advantageous for responding to theminiaturization of the flexural vibration piece.

Accordingly, it is possible to provide a small flexural vibration piecein which a reduction in Q value is suppressed and vibrationcharacteristics are stabilized.

Second Application

A second application of the invention is directed to a flexuralvibration piece including: a flexural vibrator that has a first regionon which a compressive stress or a tensile stress acts due to vibrationand a second region having a relationship in which a tensile stress actsthereon when a compressive stress acts on the first region and acompressive stress acts thereon when a tensile stress acts on the firstregion, and performs flexural vibration in a first plane; and a heatconduction path, in the vicinity of the first region and the secondregion, that is formed of a material having a thermal conductivityhigher than that of the flexural vibrator and thermally connects betweenthe first region and the second region, wherein when m is the number ofheat conduction paths, α_(th) is the thermal conductivity of the heatconduction path, α_(v) is the thermal conductivity of the flexuralvibrator, t_(v) is the thickness of the flexural vibrator in a directionorthogonal to the first plane, and t_(th) is the thickness of the heatconduction path, a relationship of t_(th)≧(t_(v)/m)×(α_(v)/α_(th)) issatisfied.

The present inventor has found that according to the configuration, athermal relaxation time required for the temperature difference causedbetween the first region and the second region reaching a state ofequilibrium is shortened due to the heat conduction path having athermal conductivity higher than that of the flexural vibrator, andtherefore a reduction in Q value is suppressed.

Third Application

A third application of the invention is directed to the flexuralvibration piece according to the above-described application of theinvention, wherein the flexural vibrator is formed so as to extend fromone end of a base, and the heat conduction path is formed so as to passover the base near the root of the flexural vibrator at the base.Moreover, in the flexural vibration piece according to theabove-described application of the invention, a first electrode isformed in at least part of the first region, a second electrode isformed in at least part of the second region, and the heat conductionpath is connected to the first electrode and the second electrode.

The present inventor has found that according to the configuration, theheat conduction path can be formed more easily compared to the casewhere the heat conduction path is disposed in the vibration arm.

Fourth Application

A fourth application of the invention is directed to the flexuralvibration piece of the above-described application of the invention,wherein when l_(th) is the length of the heat conduction path, and l_(v)is the distance between the first region and the second region of theflexural vibrator, a relationship of t_(th)(t_(v)/m)×(α_(v)/α_(th))×(l_(th)/l_(v)) is satisfied.

The present inventor has found that by defining the length or thicknessof the heat conduction path so as to satisfy the relationship of theformula, an effect of suppressing the heat conduction loss can beprovided more reliably.

Fifth Application

A fifth application of the invention is directed to the flexuralvibration piece of the above-described application of the invention,wherein when f₀ is the thermal relaxation frequency of the flexuralvibration piece in a state where the heat conduction path is notdisposed, a relationship of 1>fr/(f₀+(f₂₀−f₀)/3) is satisfied. In theflexural vibration piece of the above-described application of theinvention, wherein when fr is a mechanical oscillation frequency of theflexural vibrator, f₂₀ is a thermal relaxation frequency of the flexuralvibration piece, π is a ratio of the circumference of a circle to itsdiameter, k is a thermal conductivity of a material used for theflexural vibrator in a vibration direction, ρ is a mass density of amaterial used for the flexural vibrator, C_(p) is a heat capacity of thematerial used for the flexural vibrator, a is the width of the flexuralvibrator in the vibration direction, and f₀=πk/(2ρC_(p)a²), arelationship of 1>fr/(f₀+(f₂₀−f₀)/3) is satisfied.

The present inventor has found that according to the configuration, itis possible to provide a flexural vibration piece assuring a Q valuehigher than that of a flexural vibration piece of the related-artstructure and having stable vibration characteristics.

Sixth Application

A sixth application of the invention is directed to the flexuralvibration piece of the above-described application of the invention,wherein when fr is a mechanical oscillation frequency of the flexuralvibrator, π is a ratio of the circumference of a circle to its diameter,k is a thermal conductivity of a material used for the flexural vibratorin a vibration direction, ρ is a mass density of a material used for theflexural vibrator, C_(p) is a heat capacity of the material used for theflexural vibrator, a is a width of the flexural vibrator in thevibration direction, and f₀=πk/(2ρC_(p)a²), a relationship of 1≧fr/f₀ issatisfied.

According to the configuration, it is possible to provide a flexuralvibration piece assuring a high Q value and having stable vibrationcharacteristics.

Seventh Application

A seventh application of the invention is directed to the flexuralvibration piece of the above-described application of the invention,wherein when τ₀ is a thermal relaxation time required for a temperaturebetween the first region and the second region reaching a state ofequilibrium in the case where the heat conduction path is not disposed,and τ₁ is the thermal relaxation time in the case where the heatconduction path is disposed, a relationship of τ₁<τ₀ is satisfied; andwhen f₀ is the thermal relaxation frequency of the flexural vibratordetermined by 1/(2πτ₀), and fr is the mechanical resonant frequency ofthe flexural vibrator, a relationship of 1≧fr/f₀ is satisfied.

According to the configuration, since the thermal relaxation frequencyf₂₀ is higher than the mechanical resonant frequency fr, a relationshipof 1=fr/f₀ in which the Q value becomes minimum can be avoided.Therefore, it is possible to provide a flexural vibration piece in whichthe Q value is improved.

Eighth Application

An eighth application of the invention is directed to the flexuralvibration piece of the above-described application of the invention,wherein all or a part of the heat conduction path is formed by burying amaterial having a thermal conductivity higher than that of the flexuralvibrator into a through hole that penetrates from the first region tothe second region of the flexural vibrator or a through hole thatpenetrates in the vicinity of the first region and the second region.

According to the configuration, since it is possible to further shortenthe heat conduction path that thermally connects between the firstregion and the second region, the Q value can be further stabilized.

Ninth Application

A ninth application of the invention is directed to the flexuralvibration piece of the above-described application of the invention,wherein the flexural vibrator is formed of a base and vibration armsextending from one end portion of the base, and the heat conduction pathis disposed so as to go through the base.

According to the configuration, the heat conduction path can be formedmore easily compared to the case where the heat conduction path isdisposed in the vibration arm. For example, in the case of the heatconduction path according to the above-described application, which isformed of the through hole and the material having a high thermalconductivity buried in the through hole, the base having a large areafacilitates a hole making process.

Tenth Application

A tenth application of the invention is directed to an oscillator atleast including: the flexural vibration piece according to theabove-described application of the invention; and an oscillator circuitthat drives the flexural vibration piece.

According to the configuration, it is possible to provide a smalloscillator having stable oscillation characteristics because theoscillator includes the flexural vibration piece in which a reduction inQ value is suppressed as shown in the above-described application of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1 is a plan view of one main surface side for schematicallyexplaining an embodiment of a tuning fork-type quartz vibration piece asa flexural vibration piece.

FIG. 2 is a plan view of the other main surface side for schematicallyexplaining the embodiment of the tuning fork-type quartz vibrationpiece.

FIG. 3 is a side view of the tuning fork-type quartz vibration pieceviewed from an arrow in FIG. 1.

FIG. 4 is a table showing materials applicable to a heat conduction pathof the tuning fork-type quartz vibration piece and the thermalconductivities of the materials.

FIG. 5 is a plan view for schematically explaining a tuning fork-typequartz vibration piece of a first modification.

FIG. 6 is a cross-sectional view taken along line A-A in FIG. 5 forschematically explaining the tuning fork-type quartz vibration piece ofthe first modification.

FIG. 7 is a plan view for schematically explaining a tuning fork-typequartz vibration piece of a second modification.

FIG. 8 is a cross-sectional view taken along line B-B in FIG. 7 forschematically explaining the tuning fork-type quartz vibration piece ofthe second modification.

FIG. 9A is a perspective view for schematically showing a flexuralvibration piece having three vibration arms and showing a process ofelectrode formation.

FIG. 9B is a perspective view for schematically showing the flexuralvibration piece and showing a process of electrode formation.

FIG. 9C is a perspective view for schematically showing the flexuralvibration piece and showing a process of electrode formation.

FIG. 9D is an enlarged view of the front surface around the connectionof a base and the vibration arms in FIG. 9A.

FIG. 9E is an enlarged view (transparent view from the upper surface) ofthe rear surface around the connection of the base and the vibrationarms in FIG. 9A.

FIG. 9F is a cross-sectional view taken along line A-A′ in FIG. 9C.

FIG. 10 is a plan view showing a typical example of a related-art tuningfork-type quartz vibration piece.

FIG. 11 is a graph showing the relationship between the relaxationfrequency and minimum Q value in a flexural vibration piece in aflexural vibration mode.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, an embodiment in which a flexural vibration piece of theinvention is embodied in a tuning fork-type quartz vibration piece willbe described with reference to the drawings.

FIGS. 1 to 3 schematically explain a tuning fork-type quartz vibrationpiece of the embodiment. FIG. 1 is a plan view of one main surface side.FIG. 2 is a plan view of the other main surface side. FIG. 3 is a sideview viewed from the direction of an arrow 53 a in FIG. 1. In FIGS. 1and 2, electrode portions such as excitation electrodes are hatched forthe convenience of clearly showing the configuration of each part, andthe hatching does not show metal cross sections.

In FIG. 1, a tuning fork-type quartz vibration piece 50 of theembodiment is formed to have a so-called tuning fork-type external shapewith a base 52 that is formed by processing a flexural vibrator materialand a pair of vibration arms 53 and 54 bifurcated from one end side (anupper end side in the drawing) of the base 52 and extending in parallelto each other. As the flexural vibrator material, a material cut outfrom a single crystal of quartz is used in the same manner as in arelated-art tuning fork-type quartz vibration piece. For example, thematerial is formed from a so-called Z-cut quartz thin plate with theY-axis of crystal axis of quartz being directed to a longitudinaldirection of the vibration arms 53 and 54, the X-axis being directed toa width direction of the vibration arms, and the Z-axis being directedto a vertical direction of the front and rear main surfaces of thevibration piece. The tuning fork-type external shape of the tuningfork-type quartz vibration piece 50 can be precisely formed by wetetching with hydrofluoric acid solution or dry etching a quartzsubstrate material such as a quartz wafer, for example.

For suppressing the CI value, linear grooves 46A and 47A each having abottom are respectively formed on one main surfaces of the vibrationarms 53 and 54 along a longitudinal direction. Excitation electrodes 36Aand 37A are formed on the respective surfaces, including the bottomsurfaces, of the grooves 46A and 47A. In the vicinity of the other endside of the base 52 different from the one end side from which thevibration arms 53 and 54 are extended, external connection electrodes 66and 67 serving for external connection are disposed. The externalconnection electrodes 66 and 67 respectively correspond to theexcitation electrodes 36A and 37A. In the embodiment, the excitationelectrode 37A is connected to the external connection electrode 67 witha routing wire 57A including a heat conduction path 57 (described indetail later). The excitation electrode 36A is led through a connectionelectrode 36C and then connected to the other external connectionelectrode 66 via a routing wire 56C that is connected to alater-described connection electrode 56A formed on the other mainsurface.

The routing wire 36C is led from one end portion of the excitationelectrode 36A of the vibration arm 53 on the opposite side from the base52. The routing wire 36C connects between the excitation electrode 36Aand a later-described excitation electrode 36B (refer to FIGS. 2 and 3)disposed on the main surface (the other main surface) on the oppositeside from the surface on which the excitation electrode 36A is formed.

A routing wire 37C is led from one end portion of the excitationelectrode 37A of the vibration arm 54 on the opposite side from the base52. The connection electrode 37C connects between the excitationelectrode 37A and a later-described excitation electrode 37B (refer toFIG. 2) disposed on the main surface (the other main surface) on theopposite side from the surface on which the excitation electrode 37A isformed.

Similarly, as shown in FIG. 2, linear grooves 46B and 47B each having abottom are respectively formed on the other main surfaces of thevibration arms 53 and along a longitudinal direction. The excitationelectrodes 36B and 37B are disposed on the respective surfaces,including the bottom surfaces, of the grooves 46B and 47B.

The excitation electrode 368 of the vibration arm 53 is connected to theexcitation electrode 36A (refer to FIGS. 1 and 3) with the routing wire36C led from one end portion of the vibration arm 53 on the oppositeside from the base 52 by way of the side surface side of the vibrationarm 53. The excitation electrode 36A is disposed on the main surface(the one main surface) on the opposite side from the surface on whichthe excitation electrode 36B is formed. The excitation electrode 36B isalso connected to the external connection electrode 66 (refer to FIG. 1)by way of the routing wire 56A and the routing wire 56C disposed on theside surface of the base 52. The connection electrode 56A is led fromone end portion of the excitation electrode 36B on the base 52 side andincludes a later-described heat conduction path 56. The externalconnection electrode 66 is formed on the base 52 on the main surface(the one main surface) side on the opposite side from the surface onwhich the excitation electrode 36B of the tuning fork-type quartzvibration piece 50 is formed.

The excitation electrode 37B of the vibration arm 54 is connected to theexcitation electrode 37A (refer to FIG. 1) with the routing wire 37Cthat is led from one end portion of the excitation electrode 37B of thevibration arm 54 on the opposite side from the base 52 by way of theside surface side of the vibration arm 54. The excitation electrode 37Ais disposed on the main surface on the opposite side from the surface onwhich the excitation electrode 37B is formed.

The above-described electrodes and wires can be formed as follows. Afteretching quartz to form the external shape of the tuning fork-type quartzvibration piece 50, an electrode layer of gold (Au), for example, isdeposited by deposition or sputtering on an under layer of nickel (Ni)or chromium (Cr), for example. Thereafter, the electrode layer ispatterned by photolithography. However, the metal material for otherelectrodes and wires is sometimes selected for their formation inaccordance with the metal material for forming the heat conduction paths56 and 57 as will be described in detail later.

Here, the heat conduction paths 56 and 57 that serve particularly as anessential part in the configuration of the invention in the tuningfork-type quartz vibration piece 50 of the embodiment will be describedin detail.

In FIGS. 1 and 3, the heat conduction path 57 is formed on the base 52in the vicinity of the root of the vibration arm 53 at the base 52. Theheat conduction path 57 is connected to side surface electrodes 26A and26B respectively disposed on both side surfaces of the vibration arm 53orthogonal to the main surface thereof on which the excitation electrode36A is formed. The side surface electrodes 26A and 26B are formed inregions respectively including a first region 110 and a second region111 as the roots of the vibration arm 53 at the base 52 in a flexuralvibration direction indicated by the arrow in the drawing. With thisconfiguration, the heat conduction path 57 thermally connects betweenthe first region 110 and the second region 111. In addition in theembodiment, the heat conduction path 57 serves as a relay connectingportion of an inter-terminal (inter-electrode) metal that connectsbetween the excitation electrode 37A of the vibration arm 54 and theexternal connection electrode 67 together with the routing wire 57A.

Similarly, as shown in FIG. 2, in the tuning fork-type quartz vibrationpiece 50 of the embodiment, the heat conduction path 56 is formed on thebase 52 in the vicinity of the root of the vibration arm 54 at the base52. The heat conduction path 56 is connected to side surface electrodes27A and 27B respectively disposed on both side surfaces of the vibrationarm 54 orthogonal to the main surface thereof on which the excitationelectrode 37B is formed. The side surface electrodes 27A and 27B areformed in regions respectively including a first region 112 and a secondregion 113 as the root of the vibration arm 54 at the base 52 in theflexural vibration direction indicated by the arrow in the drawing. Theheat conduction path 56 thermally connects between the first region 112and the second region 113. In addition, the heat conduction path 56serves as a relay metal portion that connects the connection electrode56A led from the excitation electrode 36B of the vibration arm 53 withthe external connection electrode 66 shown in FIG. 1 and the connectionelectrode 56C led from the external connection electrode 66.

In many cases, the side surface electrodes 26A, 26B, 27A, and 27B areusually used as parts of relay electrodes that connect various types ofcorresponding electrodes to each other on both the main surfaces of thetuning fork-type quartz vibration piece 50. In the embodiment, however,the illustration and description thereof is omitted.

A material having a high thermal conductivity is used for the heatconduction paths 56 and 57. The material is selected in view of relativeeasiness of availability, low cost, easiness of manufacturing whenforming the heat conduction paths 56 and 57 on the flexural vibrator,and the like, in addition to the thermal conductivity. For example, thematerials shown in FIG. 4 are preferably used. For enhancing the filmadhesiveness of the heat conduction paths 56 and 57 with at least one ofthe base 52 and the vibration arms 53 and 54, an under film made ofnickel (Ni), chromium (Cr), or the like may be disposed as an underlayer of the heat conduction paths 56 and 57.

In the embodiment, the heat conduction paths 56 and 57 have to be aconductor because they serve also as the relay wiring portion of aninter-electrode wire. Therefore, diamond in the drawing is excluded.However, when the heat conduction path is formed separately from therouting wire, conductivity is not required for the material of the heatconduction path. Therefore, a non-conductive material having a highthermal conductivity, such as diamond in the drawing, can be properlyused.

In FIG. 1, when a drive voltage is applied from an oscillator circuit(not shown) as exciting means connected to the outside to the excitationelectrodes 36A and 363 and the excitation electrodes 37A and 37B in thetuning fork-type quartz vibration piece 50, the vibration arms 53 and 54horizontally perform flexural vibration toward each other and away fromeach other as indicated by the arrows in the drawing. In the embodiment,it can be said that the base 52 and the vibration arms 53 and 54 areformed on a predetermined first plane, and that the vibration arms 53and 54 perform flexural vibration in the first plane.

Due to the flexural vibration, in the connections between the base 52and the respective vibration arms 53 and 54, a compressive stress and atensile stress occur in the regions of the root portions of therespective vibration arms 53 and 54 in the vibration direction. That is,a compressive stress and a tensile stress occur in the first region 110and the second region 111 of the vibration arm 53 in the drawing.Similarly to this, a compressive stress and a tensile stress occur alsoin the region of the connection of the vibration arm 54 with the base 52(described in detail later). Description will be made in detail on thevibration arm 53 side in the drawing. When a free end side of thevibration arm 53 performs flexural vibration toward the vibration arm54, a tensile stress acts on the first region 110 of the vibration arm53 to decrease temperature, and a compressive stress acts on the secondregion 111 to increase temperature. Conversely, when the free end sideof the vibration arm 53 bends away from the vibration arm 54, acompressive stress acts on the first region 110 to increase temperature,and a tensile stress acts on the second region 111 to decreasetemperature.

Similarly, in FIG. 2, when a free end side of the vibration arm 54performs flexural vibration toward the vibration arm 53, a tensilestress acts on the first region 112 of the vibration arm 54 to decreasetemperature, and a compressive stress acts on the second region 113 toincrease temperature. Conversely, when the free end side of thevibration arm 54 bends away from the vibration arm 53, a compressivestress acts on the first region 112 to increase temperature, and atensile stress acts on the second region 113 to decrease temperature.

In this manner, inside the connections of the respective vibration arms53 and 54 with the base 52, a temperature gradient is generated betweenthe portion on which a compressive stress acts and the portion on whicha tensile stress acts. The gradient changes in direction depending onthe vibration direction of the vibration arms 53 and 54.

Due to the temperature gradient, heat conducts from the portion on thecompression side to the portion on the tensile (extension) side, thatis, from the portion on the high-temperature side to the portion on thelow-temperature side.

In the tuning fork-type quartz vibration piece 50 of the embodiment, theheat conduction path from the portion on the compression side to theportion on the extension side is assured by the heat conduction path 57(refer to FIGS. 1 and 3) in the vibration arm 53 and assured by the heatconduction path 56 (refer to FIG. 2) in the vibration arm 54. The heatconduction paths 56 and 57 are configured of a material having a thermalconductivity at least higher than that of quartz as the flexuralvibrator. Therefore, the time for heat conduction from the compressionside to the extension side is faster than in the case of a related-artstructure in which the heat conduction paths 56 and 57 are not disposed.That is, a relaxation time τ₁ required for the temperature reaching astate of equilibrium between the first regions 110 and 112 and thesecond regions 111 and 113 when the vibration arms 53 and 54 performflexural vibration is shorter than a relaxation time τ₀ of therelated-art structure in which the heat conduction paths 56 and 57 arenot disposed. That is, since τ₁<τ₀ is established in a thermalrelaxation frequency f₂₀=1/(2πτ₁) of the tuning fork-type quartzvibration piece 50 of the embodiment, the thermal relaxation frequencyf₂₀ in the embodiment is higher than a thermal relaxation frequencyf₀=1/(2πτ₀) of the tuning fork-type quartz vibration piece having therelated-art structure.

It is generally known that the thermal relaxation frequency f₀ isdetermined by the following equation (1):

f ₀ =πk/(2ρC _(p) a ²)  (1)

where π is the ratio of the circumference of a circle to its diameter, kis the thermal conductivity of a vibration arm (flexural vibrator) in aflexural vibration direction, ρ is the mass density of the vibration arm(flexural vibrator), C_(p) is the heat capacity of the vibration arm(flexural vibrator), and a is the width of the vibration arm (flexuralvibrator) in the flexural vibration direction. When constants of amaterial itself of the vibration arm are input to the thermalconductivity k, mass density ρ, and heat capacity C_(p) of the equation(1), the thermal relaxation frequency f₀ to be determined is arelaxation oscillation frequency of a flexural vibrator in which theheat conduction paths that thermally connect between the first regions110 and 112 and the second regions 111 and 113 are not disposed.

In terms of the relationship between the mechanical oscillationfrequency (resonant frequency) and Q value of the vibration arm in FIG.11, since the shape of the curve F itself is not changed, the curve F isshifted to the position of the curve F₂ in a frequency increasingdirection along with an increase in thermal relaxation frequency.Accordingly, in a range in which fr is equal to or less than the thermalrelaxation frequency f₀, that is, in a range satisfying a relationshipof 1≧fr/f₀ where fr is the mechanical oscillation frequency (resonantfrequency) of the vibration arm, the Q value on the curve F₂ is alwayshigher than that on the curve F of the tuning fork-type quartz vibrationpiece of the related-art structure. In addition, also in a frequencyband at a frequency lower than that at an intersection of the curve Fand the curve F₂, that is, in a range satisfying a relationship of1>fr/(f₀+(f₂₀−f₀)/3) on the curve F₂, the Q value is higher than that onthe curve F of the tuning fork-type quartz vibration piece having therelated-art structure. In this manner, in the tuning fork-type quartzvibration piece 50 of the embodiment, the heat conduction paths 56 and57 that thermally connect between the first regions 110 and 112 and thesecond regions 111 and 113 of the vibration arms 53 and 54 are disposed,so that it is possible to improve the Q value and realize highperformance.

In this case, the heat conduction paths 56 and are formed in thevicinity of the first regions 110 and 112 and the second regions 111 and113 of the base 52 so that the thermal relaxation between the firstregions 110 and 112 and the second regions 111 and 113 where theincrease or decrease in temperature along with the flexural vibration ofthe vibration arms 53 and 54 is caused is performed in a short time.

The present inventor has found in the configuration of the tuningfork-type quartz vibration piece 50 of the embodiment that an effect ofsuppressing a reduction in Q value due to the heat conduction path isprovided by satisfying a relationship of t_(th)≧(t_(v)/m)×(α_(v)/α_(th))when m is the number of heat conduction paths in each of the vibrationarms 53 and 54 having the first region and the second region, α_(th) isthe thermal conductivity of a material used for the heat conductionpaths 56 and 57, α_(v) is the thermal conductivity of the flexuralvibrator (quartz in the embodiment), t_(v) is the thickness of thevibration arms 53 and 54 in a direction orthogonal to a flexuralvibration direction, and t_(th) is the thickness of the heat conductionpaths 56 and 57 in the direction orthogonal to the flexural vibrationdirection of the vibration arms 53 and 54. That is, by satisfying thecondition, it is possible to avoid an unfavorable state in which heatconducts more easily in the flexural vibrator (quartz in the embodiment)than in the heat conduction paths 56 and 57. It is preferable to satisfya relationship of t_(th)>(t_(v)/m)×(α_(v)/α_(th)). With this condition,it is possible to reliably realize a state in which heat conducts moreeasily in the heat conduction paths 56 and 57 than in the flexuralvibrator (quartz in the embodiment), so that the improvement of the Qvalue caused by shortening the thermal relaxation time is reliablyachieved.

For example, in the tuning fork-type quartz vibration piece 50 of theembodiment, in the case where the thermal conductivity α_(v) of theflexural vibrator when using a so-called Z-cut quartz is 6.2 Wm⁻¹K⁻¹,the thermal conductivity α_(th) when using gold for the heat conductionpaths 56 and 57 is 315 Wm⁻¹K⁻¹, the number m of heat conduction paths ineach of the vibration arms 53 and 54 when disposing only on one mainsurface side is one, and the thickness t_(v) of the vibration arms 53and 54 in the direction orthogonal to the flexural vibration directionis 100 μm, if the thickness of the heat conduction paths 56 and 57 isensured to be 2 μm or more, a reduction in Q value can be suppressedcompared to the case where the heat conduction paths 56 and 57 are notdisposed.

In the embodiment, the heat conduction path 56 or 57 by the number m=1is disposed on one of main surface sides of each of the vibration arms53 and 54. This is not restrictive. It is possible to dispose the heatconduction path on both main surfaces of each of the vibration arms sothat m=2. Moreover, it is also possible to dispose the heat conductionpath on both main surfaces of each of the vibration arms and alsodispose the heat conduction path by using a later-described through holeso that m=3. As the number m of the heat conduction paths is larger, themore heat conducts easily through the heat conduction path whiledecreasing the rate of going through the flexural vibrator. Therefore,it is apparent that a thermal relaxation time τ can be efficientlyshortened. For example, in the case where the thermal conductivity α_(v)of the flexural vibrator is 6.2 Wm⁻¹K⁻¹, the thermal conductivity α_(th)of the heat conduction path is 315 Wm⁻¹K⁻¹, the thickness t_(v) of thevibration arms in the direction orthogonal to the vibration direction is100 μm, and the number m of the heat conduction paths when disposing oneheat conduction path on both main surfaces of each of the vibration armsis two, it is sufficient to ensure the thickness of the heat conductionpath to be 1 μm or more.

The present inventor also has found that by satisfying a relationship oft_(th)≧(t_(v)/m)×(α_(v)/α_(th))×(l_(th)/l_(v)) when l_(th) is the lengthof the heat conduction path, and l_(v) is the heat conduction pathlength between the first region and the second region, an effect ofsuppressing a reduction in Q value due to the heat conduction path ismore reliably provided. That is, the present inventor has found thatwhen the length l_(th) of the heat conduction path is large, it isnecessary to shorten the thermal relaxation time by increasing thethickness t_(th) of the heat conduction paths 56 and 57 corresponding tothe length.

In FIG. 1 for example, the path length l_(th) of the heat conductionpath 57 from the first region 110 to the second region 111 in thevibration arm 53 of the embodiment is expressed as l_(th)=l(a)+l(b)+l(c)as indicated by the dimension lines and reference signs in the drawing.On the other hand, in the case where the heat conduction path is formedon the side surface portion of the vibration arm, which is used as theforming region of the wiring path in the related art, when the pathlength l_(th0) of the heat conduction path is indicated by the dimensionlines and reference signs in the drawing, l_(th0)=l_(v)+2×l(d) (wherel_(v) is the width of the vibration arm 53 in a direction parallel tothe vibration direction, and l(d) is the length from the root of thevibration arm 53 at the base 52 to the tip end on the free end side).

Specifically, in the case where l(a)=50 μm, l(b)=50 μm, and l(c)=50 μmwith the dimensions of the vibration arm 53 as l_(v)=50 μm (=l(b)) andl(d)=1500 μm, the path length is 3050 μm when the heat conduction pathis disposed by utilizing the side surface of the vibration arm 53,whereas the path length of the heat conduction path 57 of the embodimentis 150 μm. Compared to the related-art heat conduction path length, itis understood that the heat conduction paths 56 and 57 of the embodimentcan be considerably shortened.

In the embodiment, parts of the routing wires connecting between theexcitation electrodes 36A, 36B, 37A, and 37B and the external connectionelectrodes 66 and 67 corresponding thereto are used as the heatconduction paths 56 and 57. With this configuration, measures forstabilizing the Q value can be taken with high space efficiency.Therefore, the configuration is advantageous for the miniaturization ofthe tuning fork-type quartz vibration piece 50.

The tuning fork-type quartz vibration piece as the flexural vibrationpiece described in the embodiment can be implemented as the followingmodifications.

First Modification

In the embodiment, the heat conduction paths 56 and 57 are disposed onthe main surface of the base 52 of the flexural vibrator. This is notrestrictive, and the heat conduction path may be buried in a throughhole disposed inside the flexural vibrator.

FIGS. 5 and 6 schematically explain a modification of a tuning fork-typequartz vibration piece in which heat conduction paths are disposedinside a flexural vibrator. FIG. 5 is a plan view of one main surfaceside. FIG. 6 is a cross-sectional view taken along line A-A in FIG. 5.FIG. 5 is the plan view of the same main surface side as that of FIG. 1.In FIGS. 5 and 6 of the modification, the same constituent as in theembodiment is denoted by the same reference numeral and sign, and thedescription thereof is omitted.

In FIG. 5, a tuning fork-type quartz vibration piece 150 of themodification is formed of the base 52 formed of a flexural vibratormaterial and the pair of vibration arms 53 and 54 bifurcated from oneend side of the base 52 and extending in parallel to each other. Thegrooves 46A and 47A each having a bottom are formed on the respectivemain surfaces of the vibration arms 53 and 54. The excitation electrodes36A and 37A are formed on the respective surfaces, including the bottomsurfaces, of the grooves 46A and 47A. In the vicinity of the other endside of the base 52 different from the one end side from which thevibration arms 53 and 54 are extended, the external connectionelectrodes 66 and 67 are disposed. The external connection electrodes 66and 67 respectively correspond to the excitation electrodes 36A and 37A.The excitation electrode 37A is connected to the external connectionelectrode 67 with a routing wire 157. The excitation electrode 36A isled through the connection electrode 36C and then connected to theexternal connection electrode 66 via the routing wire formed on theother main surface in the same manner as the embodiment.

Excitation electrodes as counter electrodes of the excitation electrodes36A and 37A are respectively disposed on the main surfaces (the othermain surfaces) of the vibration arms 53 and 54 on the opposite side inthe same manner as the embodiment. The excitation electrodes formed onboth the main surfaces of the respective vibration arms 53 and 54 areconnected to each other with the connection electrodes 36C and 37C.

The side surface electrodes 26A and 26B are respectively disposed onboth side surfaces of the vibration arm 53 orthogonal to the mainsurface thereof on which the excitation electrode 36A is formed. In thevicinity of the root portion of the vibration arm 53 at the base 52, aheat conduction path 116 is disposed. The heat conduction path 116 isformed by burying a material having a high thermal conductivity shown inFIG. 4, for example, into a through hole that penetrates in the samedirection as the flexural vibration direction of the vibration arm 53.As shown in FIG. 6, the side surface electrodes 26A and 26B of thevibration arm 53 are thermally connected to each other with the heatconduction path 116.

Similarly, the side surface electrodes 27A and 27B are respectivelydisposed on both side surfaces of the other vibration arm 54 orthogonalto the main surface thereof on which the excitation electrode 37A isformed. In the vicinity of the root portion of the vibration arm at thebase 52, a heat conduction path 117 is disposed. The heat conductionpath 117 is formed by burying a material having a high thermalconductivity into a through hole that penetrates in the same directionas the flexural vibration direction of the vibration arm 54. Therefore,the side surface electrodes 27A and 27B are thermally connected to eachother.

According to the configuration, since a thermal relaxation time τ1between the regions (the first region and the second region) where theincrease or decrease in temperature is caused along with the flexuralvibration of the vibration arms 53 and 54 is shortened, an effect ofstabilizing the Q value of the tuning fork-type quartz vibration piece150 is provided.

In the tuning fork-type quartz vibration piece 150 of the firstmodification, when there is a need to electrically connect between theside surface electrodes 26A and 26B of the vibration arm 53 and betweenthe side surface electrodes 27A and 27B of the vibration arm 54, a metalmaterial having conductivity among the materials having a high thermalconductivity shown in FIG. 4, for example, may be used as the materialto be buried into the through hole of the heat conduction paths 116 and117.

When there is no need to electrically connect between the side surfaceelectrodes 26A and 26B of the vibration arm 53 and between the sidesurface electrodes 27A and 27B of the vibration arm 54, the material tobe buried into the through hole of the heat conduction paths 116 and 117may not have conductivity. Moreover, the side surface electrodes 26A,26B, 27A, and 27B may not be disposed.

Second Modification

In the tuning fork-type quartz vibration piece 150 of the firstmodification, the heat conduction paths 116 and 117 are formed byburying a material having a relatively high thermal conductivity intothe through hole that penetrates in the same direction as the flexuralvibration direction of the vibration arms 53 and 54, that is, in thesame direction as that in which the two vibration arms 53 and 54 arearranged in parallel. This is not restrictive. In the case of avibration piece that performs flexural vibration in a directionorthogonal to the flexural vibration direction of the vibration arms 53and 54 of the tuning fork-type quartz vibration pieces 50 and 150 of theembodiment and the first modification, a heat conduction path may bedisposed by using a through hole formed in a direction orthogonal to thethrough hole of the heat conduction paths 116 and 117 of the firstmodification. FIGS. 7 and 8 schematically explain a tuning fork-typequartz vibration piece of a second modification. FIG. 7 is a plan viewof one main surface side. FIG. 8 is a cross-sectional view taken alongline B-B in FIG. 7.

In FIG. 7, a tuning fork-type quartz vibration piece 250 of themodification is formed of a base 152 formed of a flexural vibratormaterial and a pair of vibration arms 153 and 154 bifurcated from oneend side of the base 152 and extending in parallel to each other.Grooves 146A and 147A each having a bottom are formed on respective mainsurfaces of the vibration arms 153 and 154. Excitation electrodes 136Aand 137A are formed on the respective surfaces, including the bottomsurfaces, of the grooves 146A and 147A. In the vicinity of the other endside of the base 152 different from the one end side from which thevibration arms 153 and 154 are extended, external connection electrodes166 and 167 are disposed. The external connection electrodes 166 and 167respectively correspond to the excitation electrodes 136A and 137A. Theexcitation electrode 136A is connected to the external connectionelectrode 166 via a relay electrode 126A disposed on the base 152. Theexcitation electrode 137A is connected to the external connectionelectrode 167 via a relay electrode 127A disposed on the base 152.

As shown in FIG. 8, a groove 146B having a bottom is formed on a mainsurface (the other main surface) of the vibration arm 153 on theopposite side. An excitation electrode 136B is formed on the surface,including the bottom surface, of the groove 146B. A relay electrode 126Bis formed on the base 152 at a position corresponding to the relayelectrode 126A. Similarly, although not shown in the drawing, a groovehaving a bottom is formed on a main surface of the other vibration arm154 on the opposite side, an excitation electrode is formed on thesurface, including the bottom surface, of the groove, and a relayelectrode is formed on the base 152 at a position corresponding to therelay electrode 127A.

In FIG. 8, when a drive voltage is applied to the excitation electrodes136A and 136B of the tuning fork-type quartz vibration piece 250, thevibration arm 153 performs flexural vibration in a direction indicatedby the arrow in the drawing. The flexural vibration direction isorthogonal to the flexural vibration direction of the vibration arms 53and 54 of the tuning fork-type quartz vibration pieces 50 and 150 of theembodiment and the first modification.

Similarly, although not shown in the drawing, when a drive voltage isapplied to the excitation electrode 137A and the excitation electrode asa counter electrode, the vibration arm 154 also performs flexuralvibration in the same direction as the vibration arm 153.

That is, in the tuning fork-type quartz vibration piece 250 of themodification, the relay electrodes 126A, 126B, and 127A are disposed inthe vicinity of the regions (the first region and the second region)where the increase or decrease in temperature is caused along with theflexural vibration of the vibration arms 153 and 154. In the vicinity ofthe root portion of the vibration arm 153 at the base 152, a heatconduction path 216 is disposed. The heat conduction path 216 is formedby burying a material having a high thermal conductivity shown in FIG.4, for example, into a through hole that penetrates in the samedirection as the flexural vibration direction of the vibration arm 153.As shown in FIG. 8, the relay electrodes 126A and 126B on both the mainsurfaces of the vibration arm 153 are thermally connected to each otherwith the heat conduction path 216.

Similarly, in the vicinity of the root portion of the other vibrationarm 154 at the base 152, a heat conduction path 217 is disposed. Theheat conduction path 217 is formed by burying a material having a highthermal conductivity into a through hole that penetrates in the samedirection as the flexural direction of the vibration arm 154. The relayelectrode 127A and the relay electrode facing the relay electrode 127Aare thermally connected to each other.

According to the configuration, since the thermal relaxation time τ1between the regions (the first region and the second region) where theincrease or decrease in temperature is caused along with the flexuralvibration of the vibration arms 153 and 154 is shortened, an effect ofstabilizing the Q value of the tuning fork-type quartz vibration piece250 is provided.

In the modification, the heat conduction paths 216 and 217 are disposedin the base 152 having a large area compared to the vibration arms 153and 154. This facilitates the hole making process of the through hole ofthe heat conduction paths 216 and 217.

In the modification, the heat conduction paths 216 and 217 are disposedin the base 152 for facilitating the hole making process of the throughhole. However, the heat conduction path may be disposed in the vicinityof the roots of the respective vibration arms 153 and 154 at the base152. In this case, the heat conduction path that thermally connectsbetween the regions (the first region and the second region) where theincrease or decrease in temperature is caused along with the flexuralvibration of the vibration arms 153 and 154 is further shortened, andtherefore the Q value can be further stabilized.

Oscillator

The tuning fork-type quartz vibration pieces 50, 150, and 250 asflexural vibration pieces described in the embodiment and themodifications can be applied to piezoelectric devices or variouselectronic components other than piezoelectric devices. Especially anoscillator configured by at least incorporating into a package, togetherwith any flexural vibration piece of the tuning fork-type quartzvibration pieces 50, 150, and 250, an oscillator circuit element thatoscillates the flexural vibration piece can realize high performancebecause of an improvement in Q value and can achieve miniaturization.

Although the embodiment of the invention made by the inventor has beenspecifically described so far, the invention is not restricted to theabove-described embodiment. Various changes can be added in a range notdeparting from the gist of the invention.

For example, in the tuning fork-type quartz vibration piece 50 of theembodiment, the heat conduction path 56 or 57 is disposed on one of mainsurface sides in each of the vibration arms 53 and 54. However, this isnot restrictive. For example, when the heat conduction path is disposedon both main surfaces of each of the vibration arms, the heat conductionfrom the first regions 110 and 112 to the second regions 111 and 113 ofthe vibration arms 53 and 54 is more efficiently performed. Therefore,an effect of suppressing a reduction in Q value can be improved. In thiscase, parts of the routing wires 56A and 57A are not used as the heatconduction paths 56 and 57 unlike the embodiment, but a heat conductionpath that is electrically independent of the routing wire is disposed onboth main surfaces of the vibration arms, whereby the first region andthe second region are connected to each other with the two heatconduction paths.

In the tuning fork-type quartz vibration pieces 150 and 250 of the firstand second modifications, the heat conduction paths 116 and 117 or theheat conduction paths 216 and 217 formed of a through hole and amaterial having a high thermal conductivity buried into the through holehave been described. The penetrating direction of the through hole ofthe heat conduction paths 116 and 117 or the heat conduction paths 216and 217 can be a direction orthogonal to the penetrating direction withrespect to the vibration direction of the vibration arms 53 and 54 orthe vibration arms 153 and 154. For example, the heat conduction pathcan be used also as an inter-layer wire that connects correspondingelectrodes to each other on both the main surfaces of the vibration arms53 and 54 or the vibration arms 153 and 154.

The embodiment and the modifications have described the tuning fork-typequartz vibration pieces 50, 150, and 250 as flexural vibration pieces.This is not restrictive. The flexural vibration piece of the inventionmay be a so-called beam type flexural vibration piece having a reedshape. Moreover, even when a flexural vibration piece having three ormore vibration arms can provide the same effect as in the embodiment andthe modifications.

A specific example of a flexural vibration piece having three or morevibration arms will be described below. FIGS. 9A to 9F schematicallyshow a flexural vibration piece having three vibration arms. FIGS. 9A to9C show the process of electrode formation. FIG. 9D is an enlarged viewof the front surface around the connection of a base and the vibrationarms in FIG. 9A. FIG. 9E is an enlarged view (transparent view from theupper surface) of the rear surface around the connection of the base andthe vibration arms in FIG. 9A. FIG. 9F shows a cross-sectional viewtaken along line A-A′ in FIG. 9C.

As shown in FIGS. 9A to 9F, a piezoelectric element 10 includes a base16 formed of a quartz substrate and three vibration arms 18 a, 18 b, and18 c extending from one end of the base. The vibration arms 18 a, 18 b,and 18 c include a lower electrode 20 arranged on a main surface 12, apiezoelectric film 22 arranged on the lower electrode 20, and an upperelectrode 26 arranged on the piezoelectric film 22. The vibration arms18 a and 18 c and the vibration arm 18 b alternately perform flexuralvibration vertically. In other words, it can be said that they performflexural vibration in a direction orthogonal to a plane on which thebase 16 and the vibration arms 18 a, 18 b, and 18 c are formed. A widtha of the vibration arm of this example in a vibration direction is athickness direction of the vibration arm. As shown in FIG. 9A in thisexample, the lower electrode 20 is first formed on the surface of thevibration arms 18 a, 18 b, and 18 c. As shown in FIG. 9B, thepiezoelectric film 22 is formed so as to cover parts of the lowerelectrode 20 and the base 16, and openings 24 for continuity connectionbetween the lower electrode 20 and the upper electrode 26 are formed. Asshown in FIG. 9C, the upper electrode 26 is formed on the piezoelectricfilm 22. FIG. 9F shows a cross-sectional view taken along line A-A′ inFIG. 9C. The lower electrode, the piezoelectric film, and the upperelectrode are stacked on the quartz substrate to form an electrode. Inthis case, the lower electrode 20 of the vibration arms 18 a and 18 cand the upper electrode 26 of the vibration arm 18 b are connected toeach other, and the upper electrode of the vibration arms 18 a and 18 cand the lower electrode 20 of the vibration arm 18 b are connected toeach other. In this example, the lower electrode 20 is formed of anelectrode material having a thermal conductivity higher than that of aquartz substrate.

Due to the flexural vibration, in the connections between the base 16and the vibration arms 18 a, 18 b, and 18 c, a compressive stress and atensile stress occur on the front and rear surfaces of the vibrationarms 18 a, 18 b, and 18 c in the root portions in the vibrationdirection. Description will be made in detail on the vibration arms inthe drawing. When the vibration arms 18 a and 18 c perform flexuralvibration in the +Z-axis direction, a compressive stress acts on a firstregion on the front surface of the vibration arms 18 a and 18 c toincrease temperature, and a tensile stress acts on a second region onthe rear surface to decrease temperature. On the other hand, thevibration arm 18 b performs flexural vibration in the −Z-axis direction.A tensile stress acts on the first region on the front surface of thevibration arm 18 b to decrease temperature, and a compressive stressacts on the second region on the rear surface to increase temperature.In this manner, inside the connections of the respective vibration arms18 a, 18 b, and 18 c with the base 16, a temperature gradient isgenerated between the portion on which a compressive stress acts and theportion on which a tensile stress acts. The gradient changes indirection depending on the vibration direction of the vibration arms 18a, 18 b, and 18 c. Due to the temperature gradient, heat conducts fromthe portion on the compression side to the portion on the tensile side,that is, from the high-temperature side to the low-temperature side.

In the tuning fork-type quartz vibration piece of this example, a heatconduction path 30 is extended from side surfaces of each of the lowerelectrodes 20 around the connections between the respective vibrationarms 18 a, 18 b, and 18 c and the base 16 as shown in FIG. 9D, and theheat conduction path 30 is formed so as to overlap the second region onthe rear surface as shown in FIG. 9E. Therefore, the time for heatconduction from the compression side to the tensile side is faster thanin a structure in which the heat conduction path 30 is not disposed.Although the lower electrode is used as the heat conduction path in thisexample, the piezoelectric film or the upper electrode may be used asthe heat conduction path.

Although the embodiment and the modifications have described the tuningfork-type quartz vibration pieces 50, 150, and 250 formed of quartz asan example of flexural vibration piece, the tuning fork-type quartzvibration piece may be a flexural vibration piece formed of apiezoelectric substrate other than a quartz substrate. For example, anoxide substrate such as of aluminum nitride (AlN), lithium niobate(LiNbO₃), lithium tantalate (LiTaO₃), lead zirconate titanate (PZT), orlithium tetraborate (Li₂B₄O₇) and a piezoelectric substrate configuredby stacking a thin-film piezoelectric material such as aluminum nitrideor tantalum pentoxide (Ta₂O₅) on a glass substrate can be used.Moreover, a silicon semiconductor can be used as the material of theflexural vibration piece in addition to a piezoelectric material.

The base material of a flexural vibration piece is not restricted to apiezoelectric substrate. The configuration and effect of the inventioncan be achieved not only in a piezoelectrically-actuated flexuralvibration piece using a piezoelectric substrate but also in anelectrostatically-actuated flexural vibration piece using staticelectricity force or a magnetically-actuated flexural vibration pieceusing magnetism.

The entire disclosure of Japanese Patent Application No. 2009-073740,filed Mar. 25, 2009 and No. 2010-002670, filed Jan. 8, 2010 areexpressly incorporated by reference herein.

1. A flexural vibration piece comprising: a flexural vibrator that has afirst region on which a compressive stress or a tensile stress acts dueto vibration and a second region having a relationship in which atensile stress acts thereon when a compressive stress acts on the firstregion and a compressive stress acts thereon when a tensile stress actson the first region, and performs flexural vibration in a first plane;and a heat conduction path, in the vicinity of the first region and thesecond region, that is formed of a material having a thermalconductivity higher than that of the flexural vibrator and thermallyconnects between the first region and the second region, wherein when mis the number of heat conduction paths, α_(th) is the thermalconductivity of the heat conduction path, α_(v) is the thermalconductivity of the flexural vibrator, t_(v) is the thickness of theflexural vibrator in a direction orthogonal to the first plane, andt_(th) is the thickness of the heat conduction path, a relationship oft_(th)≧(t_(v)/m)×(α_(v)/α_(th)) is satisfied.
 2. The flexural vibrationpiece according to claim 1, wherein the flexural vibrator is formed soas to extend from one end of a base, and the heat conduction path isformed so as to pass over the base near the root of the flexuralvibrator at the base.
 3. The flexural vibration piece according to claim2, wherein a first electrode is formed in at least part of the firstregion, a second electrode is formed in at least part of the secondregion, and the heat conduction path is connected to the first electrodeand the second electrode.
 4. The flexural vibration piece according toclaim 1, wherein when l_(th) is the length of the heat conduction path,and l_(v) is the distance between the first region and the second regionof the flexural vibrator, a relationship oft_(th)≧(t_(v)/m)×(α_(v)/α_(th))×(l_(th)/l_(v)) is satisfied.
 5. Theflexural vibration piece according to claim 1, wherein when fr is amechanical oscillation frequency of the flexural vibrator, f₂₀ is athermal relaxation frequency of the flexural vibration piece, π is aratio of the circumference of a circle to its diameter, k is a thermalconductivity of a material used for the flexural vibrator in a vibrationdirection, ρ is a mass density of a material used for the flexuralvibrator, C_(p) is a heat capacity of the material used for the flexuralvibrator, a is a width of the flexural vibrator in the vibrationdirection, and f₀=πk/(2ρC_(p)a²), a relationship of 1>fr/(f₀+(f₂₀−f₀)/3)is satisfied.
 6. The flexural vibration piece according to claim 1,wherein when fr is a mechanical oscillation frequency of the flexuralvibrator, π is a ratio of the circumference of a circle to its diameter,k is a thermal conductivity of a material used for the flexural vibratorin a vibration direction, ρ is a mass density of a material used for theflexural vibrator, C_(p) is a heat capacity of the material used for theflexural vibrator, a is a width of the flexural vibrator in thevibration direction, and f₀=πk/(2ρC_(p)a²), a relationship of 1≧fr/f₀ issatisfied.
 7. The flexural vibration piece according to claim 1, whereinwhen τ₀ is a thermal relaxation time required for a temperature betweenthe first region and the second region reaching a state of equilibriumin the case where the heat conduction path is not disposed, and τ₁ isthe thermal relaxation time in the case where the heat conduction pathis disposed, a relationship of τ₁<τ₀ is satisfied.
 8. The flexuralvibration piece according to claim 1, wherein all or a part of the heatconduction path is formed by burying a material having a thermalconductivity higher than that of the flexural vibrator into a throughhole that penetrates from the first region to the second region of theflexural vibrator or a through hole that penetrates in the vicinity ofthe first region and the second region.
 9. An oscillator at leastcomprising: the flexural vibration piece according to claim 1; and anoscillator circuit that drives the flexural vibration piece.